Traditional database systems optimize for performance on one-shot query processing, yet emerging large-scale monitoring applications require continuous tracking of complex data-analysis queries over collections of physically distributed streams. Given the nature of these large-scale monitoring applications, their importance for security as well as daily operations and their general applicability, surprisingly little is known about solutions for many basic distributed monitoring problems. It would be beneficial to track distributed approximate queries in a manner that is simultaneously space/time-efficient and communication-efficient.